Posts tagged topology
Zornian Functional Analysis coming to arXiv!
Oct 07 2020, 15:23
Back in autumn 2015 I took a functional analysis course with Prof. Matania Ben-Artzi, and he let me write a term paper about uses of the axiom of choice in functional analysis for my final grade. One year later, in October 2016, I finally posted the note here. It then received some feedback from some people, and about a year after that I posted a small revision.
Earlier this week I suggested my note as a source for the proof that the Baire Category Theorem is equivalent to Dependent Choice. After doing that, I stumbled upon an errata by Theo Bühler and Dietmar A. Salamon to their Functional Analysis book, which refers to my write-up.
Continue reading...Zornian Functional Analysis or: How I Learned to Stop Worrying and Love the Axiom of Choice
Oct 10 2016, 19:34
Back in the fall semester of 2015-2016 I had taken a course in functional analysis. One of the reasons I wanted to take that course (other than needing the credits to finish my Ph.D.) is that I was always curious about the functional analytic results related to the axiom of choice, and my functional analysis wasn't strong enough to sift through these papers.
I was very happy when the professor, Matania Ben-Artzi, allowed me to write a final paper about the usage of the axiom of choice in the course, instead of taking an exam.
Continue reading...When the box means nothing
May 26 2015, 10:44
When assuming the axiom of choice the product topology and box the topology are quite different when considering infinite products. For example the Tychonoff product of countably many sets of three elements is compact, metrizable an all in all a very nice space. On the other hand, the box product is not separable or second countable at all.
But without the axiom of choice the world is indeed a strange place. This was posted as answer on math.SE earlier today.
Continue reading...